Morita euivalence for nncommutative tri
Bull. Korean Math. Soc. 2000 Vol. 37, No. 2, 249-254
Chun-Gil Park
Chungnam National University
Abstract : We give an easy proof of the fact that every noncommutative torus $A_{\omega}$ is stably isomorphic to the noncommutative torus $C(\widehat{S_{\omega}}) \otimes A_{\rho}$ which has a trivial bundle structure. It is well known that stable isomorphism of two separable $C^*$-algebras is equivalent to the existence of equivalence bimodule between them, and we construct a concrete equivalence bimodule between the two stably isomorphic $C^*$-algebras $A_{\omega}$ and $C(\widehat{S_{\omega}}) \otimes A_{\rho}$.
Keywords : twisted group $C^*$-algebra, crossed product, tensor product, $C^*$-algebra bundle, equivalence bimodule
MSC numbers : Primary 46L65, 46L87
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